Multiple solutions of coupled-cluster equations for PPP model of [10]annulene

Multiple (real) solutions of the CC equations (corresponding to the CCD, ACP and ACPQ methods) are studied for the PPP model of [10]annulene, C_{10}H_{10}. The long-range electrostatic interactions are represented either by the Mataga--Nishimoto potential, or Pople's R^{-1} potential. The multiple solutions are obtained in a quasi-random manner, by generating a pool of starting amplitudes and applying a standard CC iterative procedure combined with Pulay's DIIS method. Several unexpected features of these solutions are uncovered, including the switching between two CCD solutions when moving between the weakly and strongly correlated regime of the PPP model with Pople's potential.Comment: 5 pages, 4 figures, RevTeX

Second-order electronic correlation effects in a one-dimensional metal

The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D) metal is studied at the Hartree-Fock level, and by using the second-order perturbation theory of the electronic correlation. The PPP model provides an extension of the Hubbard model by properly accounting for the long-range character of the electron-electron repulsion. Both finite and infinite version of the 1D-metal model are considered within the PPP and Hubbard approximations. Calculated are the second-order electronic-correlation corrections to the total energy, and to the electronic-energy bands. Our results for the PPP model of 1D metal show qualitative similarity to the coupled-cluster results for the 3D electron-gas model. The picture of the 1D-metal model that emerges from the present study provides a support for the hypothesis that the normal metallic state of the 1D metal is different from the ground state.Comment: 21 pages, 16 figures; v2: small correction in title, added 3 references, extended and reformulated a few paragraphs (detailed information at the end of .tex file); added color to figure

On Conformal Infinity and Compactifications of the Minkowski Space

Using the standard Cayley transform and elementary tools it is reiterated that the conformal compactification of the Minkowski space involves not only the "cone at infinity" but also the 2-sphere that is at the base of this cone. We represent this 2-sphere by two additionally marked points on the Penrose diagram for the compactified Minkowski space. Lacks and omissions in the existing literature are described, Penrose diagrams are derived for both, simple compactification and its double covering space, which is discussed in some detail using both the U(2) approach and the exterior and Clifford algebra methods. Using the Hodge * operator twistors (i.e. vectors of the pseudo-Hermitian space H_{2,2}) are realized as spinors (i.e., vectors of a faithful irreducible representation of the even Clifford algebra) for the conformal group SO(4,2)/Z_2. Killing vector fields corresponding to the left action of U(2) on itself are explicitly calculated. Isotropic cones and corresponding projective quadrics in H_{p,q} are also discussed. Applications to flat conformal structures, including the normal Cartan connection and conformal development has been discussed in some detail.Comment: 38 pages, 8 figures, late